An Optimal High-Order Tensor Method for Convex Optimization

This paper is concerned with finding an optimal algorithm for minimizing a composite convex objective function. The basic setting is that the objective is the sum of two convex functions: the first function is smooth with up to the dth-order derivative information available, and the second function is possibly nonsmooth, but its proximal tensor mappings can be computed approximately in an efficient manner. The problem is to find—in that setting—the best possible (optimal) iteration complexity for convex optimization. Along that line, for the smooth case (without the second nonsmooth part in the objective), Nesterov proposed an optimal algorithm for the first-order methods ([Formula: see text]) with iteration complexity [Formula: see text], whereas high-order tensor algorithms (using up to general dth-order tensor information) with iteration complexity [Formula: see text] were recently established. In this paper, we propose a new high-order tensor algorithm for the general composite case, with the iteration complexity of [Formula: see text], which matches the lower bound for the dth-order methods as previously established and hence is optimal. Our approach is based on the accelerated hybrid proximal extragradient (A-HPE) framework proposed by Monteiro and Svaiter, where a bisection procedure is installed for each A-HPE iteration. At each bisection step, a proximal tensor subproblem is approximately solved, and the total number of bisection steps per A-HPE iteration is shown to be bounded by a logarithmic factor in the precision required.

Weber’s Law and the Scalar Property of Timing: A Test of Canine Timing

Domestic dogs completed a temporal bisection procedure that required a response to one lever following a light stimulus of short duration and to another lever following a light stimulus of a longer duration. The short and long durations across the four conditions were (0.5–2.0 s, 1.0–4.0 s, 2.0–8.0 s, and 4.0–16.0 s). Durations that were intermediate, the training durations, and the training durations, were presented during generalization tests. The dogs bisected the intervals near the geometric mean of the short and long-stimulus pair. Weber fractions were not constant when plotted as a function of time: A U-shaped function described them. These results replicate the findings of previous research reporting points of subjective equality falling close to the geometric mean and also confirm recent reports of systematic departures from Weber’s law.

Clock Speed as a Window into Dopaminergic Control of Emotion and Time Perception

Although fear-producing treatments (e.g., electric shock) and pleasure-inducing treatments (e.g., methamphetamine) have different emotional valences, they both produce physiological arousal and lead to effects on timing and time perception that have been interpreted as reflecting an increase in speed of an internal clock. In this commentary, we review the results reported by Fayolle et al. (2015):Behav. Process., 120, 135–140) and Meck (1983: J. Exp. Psychol. Anim. Behav. Process., 9, 171–201) using electric shock and by Maricq et al. (1981: J. Exp. Psychol. Anim. Behav. Process., 7, 18–30) using methamphetamine in a duration-bisection procedure across multiple duration ranges. The psychometric functions obtained from this procedure relate the proportion ‘long’ responses to signal durations spaced between a pair of ‘short’ and ‘long’ anchor durations. Horizontal shifts in these functions can be described in terms of attention or arousal processes depending upon whether they are a fixed number of seconds independent of the timed durations (additive) or proportional to the durations being timed (multiplicative). Multiplicative effects are thought to result from a change in clock speed that is regulated by dopamine activity in the medial prefrontal cortex. These dopaminergic effects are discussed within the context of the striatal beat frequency model of interval timing (Matell & Meck, 2004:Cogn. Brain Res.,21, 139–170) and clinical implications for the effects of emotional reactivity on temporal cognition (Parker et al., 2013:Front. Integr. Neurosci., 7, 75).

Emotional Voices Distort Time: Behavioral and Neural Correlates

The present study explored the effect of vocally expressed emotions on duration perception. Recordings of the syllable ‘ah’ spoken in a disgusted (negative), surprised (positive), and neutral voice were subjected to a compression/stretching algorithm producing seven durations ranging from 300 to 1200 ms. The resulting stimuli served in a duration bisection procedure in which participants indicated whether a stimulus was more similar in duration to a previously studied 300 ms (short) or 1200 ms (long) 440 Hz tone. Behavioural results indicate that disgusted expressions were perceived as shorter than surprised expressions in both men and women and this effect was related to perceived valence. Additionally, both emotional expressions were perceived as shorter than neutral expressions in women only and this effect was related to perceived arousal. Event-related potentials showed an influence of emotion and rate of acoustic change (fast for compressed/short and slow for stretched/long stimuli) on stimulus encoding in women only. Based on these findings, we suggest that emotions interfere with temporal processes and facilitate the influence of contextual information (e.g., rate of acoustic change, attention) on duration judgements. Because women are more sensitive than men to unattended vocal emotions, their temporal judgements are more strongly distorted.

105 BOVINE DEMI-BLASTOCYSTS ARE ABLE TO EXPAND TO A SIZE SIMILAR TO INTACT BLASTOCYSTS UNTIL AT LEAST DAY 13 OF IN VITRO CULTURE

Embryo bisection has been used to produce identical twins, to increase the pregnancy rate per embryo, and for preimplantation diagnosis. However, the invasive nature of splitting might affect development decreasing embryo survival. In general, after bisection or biopsy, embryos are transferred to surrogate mothers and their competence evaluated in terms of implantation and pregnancy maintenance. However, this makes it difficult to evaluate the immediate response of each embryo to bisection. Our aim was to evaluate embryo growth during the 5 days following bisection by using an extended in vitro culture system. We postulated that bisected blastocysts are able to counteract the injury and expand in size until Day 13 of in vitro culture. Two experiments were performed. First, two different culture systems were evaluated to determine the best to support embryo development from Day 9 to 13. One system consisted of conventional culture in plastic (CCP), while the other one included co-culture with endometrial cells derived from a cycling cow (CC). Both used SOFaa supplemented with 3 mg mL–1 of fatty acid-free BSA and 2% FBS in 4-well dishes. Twenty-six nonbisected in vitro-derived blastocysts were cultured. Embryo size and survival were recorded daily. All living embryos were measured with Micrometrics™ SE Premium software and statistical analyses were performed using the Kruskal–Wallis test. From Day 9 to 11, blastocysts cultured in the CCP system had smaller diameters than those cultured in CC [Day 9: CC 358 µm, CCP 277 µm (P = 0.04); Day 10: CC 456 µm, CCP 340 µm (P = 0.005); and Day 11: CC 535 µm, CCP 408 µm (P = 0.02)]. However, on Day 12 and 13, no difference was observed in embryo diameters [(Day 12: CC 560 µm, CCP 411 µm (P = 0.1) and Day 13: CC 470 µm, CCP 474 µm (P = 0.9)]. Additionally, embryos with diameters less than 200 µm on Day 9 did not develop further independent of the culture system (P < 0.001). Thus, in the second experiment, to determine embryo size after bisection, only well-expanded grade 1 blastocysts >200 µm were used in the conventional CCP system. Twenty four Day 8 bisected (B) and nonbisected (C) blastocysts were cultured from Day 9 until 13. In the bisected group, one-half was kept for further gene expression analysis. Significant differences were observed in embryo diameter between both groups on Day 9 and 10 of culture [Day 9: B 321 µm, C 277 µm (P = 0.05); D10: B 436 µm, C 340 µm (P = 0.01)]. However, on Days 11, 12, and 13, no differences in diameter were observed (Day 11: B 411 µm, C 408 µm (P = 0.8); Day 12: B 394 µm, C 411 µm (P = 0.5); Day 13: B 316 µm, C 474 µm (P = 0.3)]. In conclusion, we show that bovine embryos are capable of developing in vitro until Day 13, and embryo diameter on Day 9 impacts on the subsequent in vitro survival of nonsplit embryos, regardless of culture system. Finally, on Day 11 of culture, the split embryos were able to overcome the injury caused by the bisection procedure and expanded in size similar to controls, until at least Day 13 of culture.

Psychophysical Assessment of Timing in Individuals With Autism

Perception of time, in the seconds to minutes range, is not well characterized in autism. The required interval timing system (ITS) develops at the same stages during infancy as communication, social reciprocity, and other cognitive and behavioral functions. The authors used two versions of a temporal bisection procedure to study the perception of duration in individuals with autism and observed quantifiable differences and characteristic patterns in participants' timing functions. Measures of timing performance correlated with certain autism diagnostic and intelligence scores, and parents described individuals with autism as having a poor sense of time. The authors modeled the data to provide a relative assessment of ITS function in these individuals. The implications of these results for the understanding of autism are discussed.